How do you find the LCM and HCF of a rational number?

How do you find the LCM and HCF of a rational number?

I was reading a text book and came across the following approach to find the LCM and HCF of rational numbers/fractions:

1. LCM of fractions = LCM of numerators/HCF of denominators.
2. HCF of fractions = HCF of numerators/LCM of denominators.

How do you find the LCM of two rational numbers?

First find the lcm of all numerator of rational number then find the gcd of all the denominator of rational number then divide lcm of all numerator/ gcd of all the denominator this the lcm of rational number’s.

What is HCF formula?

L.C.M and HCF Important Formulas H.C.F. of a given number always divides its L.C.M. To find the greatest number that will exactly divide x, y and z. Required number = HCF of x, y and z. To find the Largest number that will divide x, y and z leaving remainders a, b and c respectively.

What is the HCF of 5 15 and 25?

Factors of 25 are 1, 5 and 25. From these, we can clearly see that 1 and 5 are the factors of all three numbers i.e. 5, 15 and 25. Hence, the required common factors of 5, 15 and 25 are 1 and 5.

What is the LCD of 8 and 3?

The least common multiple of 3 and 8 is 24.

How do u find the LCM?

One way to find the least common multiple of two numbers is to first list the prime factors of each number. Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

What is rational algebraic equation?

A rational equation is an equation containing at least one fraction whose numerator and denominator are polynomials, These fractions may be on one or both sides of the equation. A common way to solve these equations is to reduce the fractions to a common denominator and then solve the equality of the numerators.

Why is LCM of a rational and an irrational number not defined?

Because rational and irrational number are number from two different set which are complement to each other means all real number which are not rational are irrational and vice versa. So there cannot be any common number between these two sets i. e. Rational and irrational therefore there HCF and LCM does not exist.

How to find the LCM or hcf of a number?

According theory of LCM and HCF to find the LCM or HCF of a and b we must write those numbers as product of powers of prime factors. Then to find HCF raise the common prime factor to the lesser of the powers in which it appears in prime factors product. Product of the above numbers is HCF.

Which is the least one in the LCM?

It is the least one because by the properties of the lcm and gcd of two integers, ∏i p max (ei ( a), ei ( c))i is the least common multiple of the numerators and ∏i p min (ei ( b), ei ( d))i is the greatest common divisor of the denominators. Hence

How to prove the GCD laws of LCM?

Here are links to proofs of the gcd laws used: law [2] and law [3]. Let 2 3, 5 6 and 7 9 be three fractions. Let A B be their LCM. Now all the fractions must divide A B, that is, A/B ÷ 2/3, A/B ÷ 5/6 and A/B ÷ 7/9 all must be natural numbers. Or A3/B2, A6/B5 and A9/B7 all must be natural numbers.